Deterioration modeling of sewer pipes via discrete-time Markov chains: A large-scale case study in the Netherlands

Sewer pipe network systems are an important part of civil infrastructure, and in order to find a good trade-off between maintenance costs and system performance, reliable sewer pipe degradation models are essential. In this paper, we present a large-scale case study in the city of Breda in the Netherlands.
Our dataset has information on sewer pipes built since the 1920s and contains information on different covariates. We also have several types of damage, but we focus our attention on infiltrations, surface damage, and cracks. Each damage has an associated severity index ranging from 1 to 5. To account for the characteristics of sewer pipes, we defined 6 cohorts of interest.
Two types of discrete-time Markov chains (DTMC), which we called Chain `Multi' and `Single' (where Chain `Multi'contains additional transitions compared to Chain `Single'), are commonly used to model sewer pipe degradation at the pipeline level, and we want to evaluate which suits better our case study. To calibrate the DTMCs, we define an optimization process using Sequential Least-Squares Programming to find the DTMC parameter that best minimizes the root mean weighted square error.
Our results show that for our case study there is no substantial difference between Chain `Multi' and `Single', but the latter has fewer parameters and can be easily trained. Our DTMCs are useful to compare the cohorts via the expected values, e.g., concrete pipes carrying mixed and waste content reach severe levels of surface damage more quickly compared to concrete pipes carrying rainwater, which is a phenomenon typically identified in practice.